Discussion of Multiscale Fisher's Independence Test for Multivariate Dependence

TL;DR

This paper discusses the multiscale Fisher's independence test (MULTIFIT), highlighting its ability to detect local dependence, handle large samples without resampling, and interpret dependency structures, while comparing it to other tests.

Contribution

It presents a unifying framework for MULTIFIT and similar tests, and compares it with the binary expansion randomized ensemble test (BERET), suggesting potential extensions.

Findings

MULTIFIT effectively detects local dependence.

The framework unifies various independence tests.

Comparison shows strengths and limitations of MULTIFIT and BERET.

Abstract

The multiscale Fisher's independence test (MULTIFIT hereafter) proposed by Gorsky & Ma (2022) is a novel method to test independence between two random vectors. By its design, this test is particularly useful in detecting local dependence. Moreover, by adopting a resampling-free approach, it can easily accommodate massive sample sizes. Another benefit of the proposed method is its ability to interpret the nature of dependency. We congratulate the authors, Shai Gorksy and Li Ma, for their very interesting and elegant work. In this comment, we would like to discuss a general framework unifying the MULTIFIT and other tests and compare it with the binary expansion randomized ensemble test (BERET hereafter) proposed by Lee et al. (In press). We also would like to contribute our thoughts on potential extensions of the method.